Virtual algebraic isomorphisms between predicate calculi of finite rich signatures. (English. Russian original) Zbl 1515.03166
Algebra Logic 60, No. 6, 389-406 (2022); translation from Algebra Logika 60, No. 6, 587-611 (2021).
Summary: It is proved that every two predicate calculi of finite rich signatures are algebraically virtually isomorphic, i.e., some of their Cartesian extensions are algebraically isomorphic. As an important application, it is stated that for predicate calculi in any two finite rich signatures, there exists a computable isomorphism between their Tarski-Lindenbaum algebras which preserves all model-theoretic properties of algebraic type corresponding to the real practice of research in model theory.
MSC:
| 03C57 | Computable structure theory, computable model theory |
| 03C07 | Basic properties of first-order languages and structures |
| 03B10 | Classical first-order logic |
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